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Laue’s Experiment: Principle, Setup and Working

Laue’s experiment demonstrates the diffraction of X-rays by crystals. Learn its principle, experimental setup, working, equations, observations and applications through this simple, step-by-step explanation.

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What Is Laue’s Experiment?

Laue’s experiment is an important experiment in physics that demonstrates the diffraction of X-rays by a crystal. In 1912, German physicist Max von Laue proposed that a crystal could diffract X-rays because its atoms are arranged in a regular, repeating three-dimensional pattern.

In this experiment, a beam of X-rays containing a range of wavelengths is directed towards a stationary single crystal. The crystal scatters the X-rays in different directions. When the scattered waves reinforce one another, they form bright spots on a photographic plate or detector.

The arrangement of these spots is called a Laue diffraction pattern. Its positions and symmetry help scientists determine the orientation and symmetry of a crystal.

Remember: Laue’s method uses polychromatic X-rays and a stationary single crystal. It is especially useful for determining crystal orientation.
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Principle of Laue’s Experiment

The experiment is based on the diffraction and constructive interference of X-rays scattered by regularly arranged atoms in a crystal. The spacing between atomic planes is comparable to the wavelength of X-rays.

Bragg’s law provides a convenient way to express the condition for constructive interference from parallel crystal planes:

nλ = 2d sin θ

Where:

  • n = order of diffraction (1, 2, 3, ...)
  • λ = wavelength of the X-rays
  • d = spacing between the relevant crystal planes
  • θ = Bragg angle, measured between the incident beam and the crystal planes

In the Laue method, the crystal remains fixed. Different wavelengths in the incident beam can satisfy the diffraction condition for different sets of crystal planes.

Important distinction: Bragg’s law is a useful description of diffraction from parallel planes. The Laue equations describe diffraction more generally using the three-dimensional crystal lattice and the incident and diffracted wave vectors.
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Experimental Setup of Laue’s Experiment

The experiment uses an X-ray source, a collimator, a stationary single crystal and a photographic plate or electronic detector.

  1. X-ray source: Produces X-rays containing a range of wavelengths.
  2. Collimator or narrow slit: Forms a narrow, directed beam.
  3. Single crystal: Is placed in the beam and kept in a fixed orientation.
  4. Photographic plate or detector: Records the diffracted X-rays as a pattern of spots.

In the transmission Laue method, the detector is placed behind the crystal. In the back-reflection Laue method, the detector records beams returning towards the incident-beam side.

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Working of Laue’s Experiment

The experiment works in the following steps:

  1. An X-ray source generates a continuous spectrum of wavelengths, commonly called white X-ray radiation.
  2. The collimator directs a narrow beam towards the crystal.
  3. The single crystal is held stationary during exposure.
  4. The atoms scatter the incident X-rays. For particular wavelengths and directions, constructive interference produces diffracted beams.
  5. A photographic plate or detector records the diffracted beams as spots.
  6. Scientists analyse the positions and symmetry of these spots to learn about crystal orientation and structure.
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Why Are Different Wavelengths Used?

White X-ray radiation contains a range of wavelengths. For a fixed crystal orientation and a particular set of crystal planes, the diffraction condition selects suitable wavelengths and directions.

Bragg’s law is: nλ = 2d sin θ. If the plane spacing and angle remain fixed, the wavelengths satisfying this equation depend on the diffraction order.

For example, if a wavelength λ satisfies the condition at first order, a wavelength λ/2 can satisfy the same geometric condition at second order, provided that wavelength is present in the incident spectrum.

This is one reason several diffraction spots can be produced while the crystal remains stationary. In the actual three-dimensional crystal, the Laue conditions determine which reciprocal-lattice points satisfy the diffraction geometry.

Diagram of Laue’s Experiment

Experimental setup of Laue’s X-ray diffraction experiment A white X-ray source sends a narrow beam through a collimator towards a stationary single crystal. Diffracted beams travel in different directions and form spots on a detector. X-ray source White radiation Collimator Narrow slit Single crystal Stationary Detector Diffraction spots

Figure 1: Simplified schematic of the transmission Laue method. The drawing is illustrative and not to scale.

The actual positions and number of diffraction spots depend on the crystal, its orientation and the X-ray spectrum.

Key Points to Remember

  • Uses polychromatic (white) X-rays.
  • The single crystal remains stationary during exposure.
  • Produces a pattern of diffraction spots.
  • Helps determine crystal orientation and symmetry.
  • Relies on X-ray diffraction and constructive interference.

Quick Facts

Scientist: Max von Laue

Year of discovery: 1912

Nobel Prize: Physics, 1914

Main purpose: X-ray diffraction by crystals

Typical sample: A single crystal

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Observations and Conclusions

  • A pattern of diffraction spots appears on the detector.
  • The spots are arranged according to the crystal’s orientation and symmetry.
  • The pattern changes when the crystal orientation changes.
  • The experiment demonstrates X-ray diffraction by crystals.
  • The pattern provides information about the crystal’s internal order.
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Applications of Laue’s Experiment

  1. Crystal orientation: Finding the orientation of a single crystal.
  2. Crystal symmetry: Studying symmetry from the arrangement of spots.
  3. Crystal quality: Detecting certain defects and distortions.
  4. Materials science: Examining single-crystal materials.
  5. Crystal alignment: Positioning crystals for further X-ray measurements.
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Advantages and Limitations

Advantages

  • The crystal remains stationary.
  • Several diffraction spots can be recorded in one exposure.
  • Useful for rapid crystal orientation.
  • Can reveal symmetry and certain imperfections.

Limitations

  • Patterns can be difficult to interpret.
  • Multiple wavelengths and diffraction orders can contribute.
  • Best suited to single-crystal samples.
  • Detailed structure analysis may require additional measurements.
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Difference Between Laue Method and Rotating-Crystal Method

Both methods use X-ray diffraction to study crystals, but they differ in the radiation used and how the diffraction data are collected.

Feature Laue Method Rotating-Crystal Method
X-ray radiation Polychromatic (a range of wavelengths) Usually monochromatic
Crystal motion Stationary during exposure Rotated during measurement
Diffraction pattern Laue spots Pattern depends on the rotation geometry
Typical use Crystal orientation and symmetry Collecting diffraction data for structural analysis

Laue’s Experiment: Exam-Ready Definition

Laue’s experiment is an experiment in which a beam of polychromatic X-rays is directed onto a stationary single crystal. The crystal diffracts the X-rays, producing a pattern of spots on a photographic plate or detector. The experiment demonstrates the diffraction of X-rays by crystals and is useful for determining crystal orientation and symmetry.

Frequently Asked Questions About Laue’s Experiment

1. Who discovered Laue’s experiment?

Max von Laue proposed the experiment in 1912. He received the Nobel Prize in Physics in 1914 for his discovery of X-ray diffraction by crystals.

2. What is the main purpose of Laue’s experiment?

It demonstrates X-ray diffraction by crystals and helps determine the orientation and symmetry of single crystals.

3. Why is white radiation used?

White X-ray radiation contains a range of wavelengths. Different wavelengths can satisfy the diffraction conditions for different sets of crystal planes.

4. Why is the crystal kept stationary?

The crystal remains in a fixed orientation during exposure. The range of incident wavelengths allows different diffraction conditions to be satisfied without rotating it.

5. What is the formula associated with Laue’s experiment?

Bragg’s law is nλ = 2d sin θ. The Laue equations provide a more general description of diffraction from a three-dimensional crystal lattice.

6. What does a Laue diffraction pattern show?

It shows the spots formed by diffracted X-rays. Their positions and symmetry provide information about crystal orientation and symmetry.

7. What is the difference between Laue and Bragg methods?

In the Laue method, polychromatic X-rays are directed at a stationary crystal. Bragg diffraction is the general diffraction condition; in common textbook comparisons, the Bragg or rotating-crystal method uses monochromatic X-rays and rotates the crystal to collect diffraction data.

Educational note: This page provides a simplified introduction to Laue diffraction. Detailed analysis of real diffraction patterns requires knowledge of crystallography and the Laue equations.